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Obj. 23 Triangle Theorems The student is able to (I can): • Identify a midsegment of a triangle and use it to solve problems. • Analyze the relationship between the angles of a triangle and the lengths of the sides • Determine allowable lengths for sides of triangles

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Identify a midsegment of a triangle and use it to solve problems. Analyze the relationship between the angles of a triangle and the lengths of the sides Determine allowable lengths for sides of triangles

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  • 1. Obj. 23 Triangle Theorems The student is able to (I can): Identify a midsegment of a triangle and use it to solve problems. Analyze the relationship between the angles of a triangle and the lengths of the sides Determine allowable lengths for sides of triangles

2. midsegmentA segment that joins the midpoints of two sides of a triangle. OPoints I, C, and E are midpoints of HOT.IC, CE, and EI are midsegments. HICET 3. Triangle Midsegment Theorem A midsegment of a triangle is parallel to a side of the triangle, and its length is half the length of that side. O1 IC HT, IC = HT 2 HICET 4. ExamplesFind each measure. 1. FE FE = 2(LT) = 2(14) = 28U L 149F2. mUFE mUFE = mTSE = 62T S62ELT and TS3. UE UE = 2(9) = 18are midsegments. 5. Thm 5-5-1If two sides of a triangle are not congruent, then the larger angle is opposite the longer side. AT > AC mC > mTThm 5-5-2If two angles of a triangle are not congruent, then the longer side is opposite the larger angle. mC > mT AT > AC CAT 6. Triangle Inequality Theorem The sum of any two side lengths of a triangle is greater than the third side length. Example: 1. Which set of lengths forms a triangle? 4, 5, 10 7, 9, 12 4 + 5 < 107 + 9 > 12 7. Note: To find a range of possible third sides given two sides, subtract for the lower bound and add for the upper bound. Examples: 2. What is a possible third side for a triangle with sides 8 and 14? 14 8 = 6 lower bound 14 + 8 = 22 upper bound The third side can be between 6 and 22. 8. 3. What is the range of values for the third side of a triangle with sides 11 and 19? 19 11 = 8 19 + 11 = 30 8 < x < 30lower bound upper bound


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